Note that Theorem REF  shows that similar to [1]}, [2]}, [3]}, [4]}, the regret under DSSL has a logarithmic order with time. DSSL, however, achieves this under the more general restless Markovian model, and also has significantly better scaling with \(M,K\)  and \(\Delta _{\min }\) . Specifically, under a common benchmark setting of equal rates among users (but still vary among channels), and \(K>M\) , which allows a theoretical comparison of learning efficiency between different algorithms, in [2]} and [1]} the regret scales as \(O(\frac{MK}{(\Delta _{\min })^2}\log (t))\)  ,in [4]} as \(O(\frac{M^3K}{(\Delta _{\min })^2}\log (t))\)  and in [3]} the regret scales as \(O(\frac{MK^2}{(\Delta _{\min })^2}\log (t))\) . In contrast, under DSSL, the regret scales as \(O((\frac{1}{(\Delta _{\min })^2}+MK)\log (t))\)  due to the novel algorithm design that explores every channel according to its unique adaptive exploration rate, while guaranteeing efficient learning.
